The universe supposedly started off with equal parts matter and antimatter and they are said to annihilate each other. Also, nature is famous for it's balance between everything. So all we see is matter and no antimatter (I guess that's a good thing, we would all have been annihilated otherwise), so where did all the antimatter go?

Also, does antimatter exist in the same space as matter? What are the leading theories about it?

Where indeed? Your question is known as the Baryon Asymmetry Problem. This is currently one of the major unsolved problems in physics, so it's clearly a good question for frontier physics. But since it hasn't been answered yet, there's really no point asking it here.
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David HJan 11 '14 at 12:50

Ah! That's why I couldn't find an answer anywhere. I thought I had missed something. And indeed the Baryon Asymmetry Problem it was.
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RanveerJan 11 '14 at 12:54

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Could probably be asked on Physics.SE, however as pointed out, there is no definitive answer yet...
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Rory AlsopJan 12 '14 at 14:16

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As long as we're clear that any proposed resolution to this riddle is purely speculation at this stage, I see no problem sharing my personal guess. I have a standing $8 bet with a colleague that when decipher the makeup of dark matter (which comprises 85% of matter in the Universe!) we'll find a reverse imbalance of dark matter particles to anti dark matter particles in such a way that exactly compensates the for the imbalance found in ordinary matter. Fingers crossed.
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David HJan 12 '14 at 21:06

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@RoryAlsop Since this question is a matter of cosmology it is firmly within scope of this site.
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called2voyage♦Jan 13 '14 at 14:32

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To answer your second question first: Yes, antimatter does exist in the same space as matter. In fact, the universe creates antimatter (and an equal amount of matter) every day as a matter of course in events like lightning strikes and supernovae, and even in certain nuclear decays. Humans create it in particle accelerators for research and for commercial/medical applications such as Positron Emission Tomography. The thing is, when we create antimatter, we also create an equal amount of matter.

In the hot flash of energy after the Big Bang, particle-antiparticle pairs were popping into existence and annihilating each other constantly. There were almost exactly equal amounts. For some reason, though, for every 100 trillion (10^11) particles of antimatter, there were 100 trillion and one particles of matter. In the ensuing few minutes, all the antimatter and all but that tiny fraction of matter annihilated each other and turned back into energy. Everything we can see today, all the galaxies, stars, and planets, are made up of that tiny amount of matter that was left over. Particle physicists still aren't sure why there was this tiny imbalance in the amount of matter and antimatter, because all interactions we've seen so far produce equal amounts of both. This is one question particle colliders like the Large Hadron Collider are attempting to answer.